Ганимедов В.Л.   Papaeva E.O.   Маслов Н.А.   Ларионов П.М.  

Numerical simulation of fluid flow in a vortex bioreactor

Reporter: Papaeva E.O.

The development of cell-mediated scaffold technologies for the treatment of critical bone defects is very important for the purpose of reparative bone regeneration. The scaffold technology could be schematically divided into two stages. The first stage is the creating of scaffold (a framework for the cells), and the second important stage is creating conditions for the cell-seeded scaffold cultivation. Today the scaffold main properties are determined to a certain degree (effective cell adhesion, osteoinductivity, elements of bone biomimetic, mechanical characteristics). Parameters of the reactor for the cell-seeded scaffold cultivation are the subject of intensive research. Mathematical modeling can help in the search for optimal reactor parameters for the cultural cultivation of scaffold: the geometry of the framework, the mechanical properties of the framework, the level of mechanical stress on cells, the concentration of nutrients, growth factors.
A polycaprolactone-based sheet with the inclusion of gelatin or chitosan, and microelements needed for osteoinduction, is proposed as a basis for the cell seeding. The scaffold sheet is seeded with cells, and then it is placed in a bioreactor for further cultivation. The simulated bioreactor schematically consists of two coaxial cylinders with different heights. The cavity of the outer cylinder is filled with liquid, and it is limited by impermeable surfaces from the ends. The flow generator in the closed cavity of the outer cylinder is the rotation around the common axis with the inner cylinder, which has a finite wall thickness and is immersed in the liquid. The scaffold sheet seeded with cells is fixed on the surfaces of the inner cylinder. This sheet is the object of influence of forces generated by the flow of the rotating liquid. To improve the quality of tissue-engineered bone equivalents, it is important to know the distribution of the shear stresses on the sample surface as a function of the rotational speed. The simulation using the ANSYS Fluent software package was carried out to evaluate it.
The system of Navier–Stokes equations was used for the mathematical description of the flow. The flow regime was postulated to be laminar. The discretization of the domain of definition and the numerical solution of the problem are constructed using the ANSYS Fluent software package. The number of elementary volumes is 3.2 million. The solution is obtained by the relaxation method.
As a result of this work, the method of flow calculating in the mathematical model of the biological reactor has been worked out. The computational algorithm shows good agreement with the analytical Couette solution for the task of two coaxial cylinders. For the reactor under study it has been found that Taylor vortices appear in the annular gap between the cylinders. The constructed mathematical model and the created computational algorithm for calculating the flow parameters allow predicting the shear stress and pressure values depending on the rotational speed, as well as optimizing the operating mode of the bioreactor.
This study was supported by the Russian Foundation for Basic Research (grant No. 15-29-04849, «Tissue-engineered bone equivalents for the replacement of bone defects with optical control based on laser-induced fluorescence spectroscopy»).

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